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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Zeta function of representations of compact $p$-adic analytic groups
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by A. Jaikin-Zapirain PDF
J. Amer. Math. Soc. 19 (2006), 91-118 Request permission


Let $G$ be an FAb compact $p$-adic analytic group and suppose that $p>2$ or $p=2$ and $G$ is uniform. We prove that there are natural numbers $n_1, \ldots , n_k$ and functions $f_1(p^{-s}),\ldots , f_k(p^{-s})$ rational in $p^{-s}$ such that \[ \zeta ^G(s)=\sum _{\lambda \in \operatorname {Irr}(G)} \lambda (1) ^{-s}=\sum _{i=1}^kn_i^{-s}f_i(p^{-s}).\]
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Additional Information
  • A. Jaikin-Zapirain
  • Affiliation: Departamento de Matemáticas, Facultad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain
  • MR Author ID: 646902
  • Email:
  • Received by editor(s): June 2, 2004
  • Published electronically: September 7, 2005
  • Additional Notes: This work has been supported by the FEDER, MEC Grant MTM2004-04665, and the Ramón y Cajal Program
  • © Copyright 2005 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 19 (2006), 91-118
  • MSC (2000): Primary 20E18; Secondary 20C15, 20G25, 22E35
  • DOI:
  • MathSciNet review: 2169043